This paper explores the ways in which Leonardo da Vinci's anachronistic skepticism of Renaissance perspective and his subsequent invention of sfumato prefigure contemporary digital technology and its ability to literalize this formal technique. Marcos Novak and Char Davies offer parallel theories on the permeable boundaries among objects and between physical and virtual worlds. The resultant theories, like those of Leonardo, offer new conceptions of space and representation that challenge those who suggest the digital world will subvert the physical. Briefly comparing Leonardo's initial revisions to Renaissance perspective to those realized through digital technology, this paper examines radical revisions of the notions of space and boundary and the ways in which those revisions challenge the traditional goal to aptly represent the physical world via linear perspective.

Every body fills the surrounding air with its likenesses, likenesses which are all in everything and all in each part.

— Leonardo da Vinci

The air we move through is permeated by intersecting emanations of information from every object: electromagnetic flux, intensities of light, pressure, and body heat form complex dancing geometries around us at every instant.

— Marcos Novak

Within the all-enveloping flux and flow, habitually perceived distinctions between things dissolve, and boundaries between interior self and exterior world become permeable and intermingled.

— Char Davies

Leonardo da Vinci was part of the Renaissance group that invested a good deal of time in developing linear perspective after Leone Battista Alberti. Unlike many of this group, however, Leonardo, as shown in his notebooks, was skeptical of linear perspective's ultimate ability to lead artists to the perennial goal of representing reality as accurately as possible. Out of this skepticism, Leonardo committed countless hours to empirical observation and eventually developed sfumato, the presentation of objects without lines or borders. Leonardo's emphasis on the dynamic and porous boundaries among objects have been taken up in profound and effective ways by contemporary digital artists Marcos Novak and Char Davies, who develop different conceptual sfumatos with new digital tools. In their respective work, Novak and Davies offer extensions and physical possibilities to Leonardo's anachronistic skepticism of Alberti's tools. In so doing these artists develop works and theories on space, its objects and their relation to representation that are some of the first that fully address Leonardo's concerns from centuries earlier [1].

Although for centuries Albertian linear perspective remained unchallenged, 20th-century technology inspired the kinds of skepticism Leonardo developed at the time of perspective's advent. Science in the 20th century became less and less dependent on empirical observations of the physical world. Atoms and genes, for example, cannot be seen. By the end of the century the advent of the digital underscored the ever-increasing divergence from the necessity of optical perspective. Lev Manovich has argued, "With the emergence of the field of computer vision, perspectival sight reaches its apotheosis and at the same time begins its retreat" [2]. Digital computers, he explains, automated linear perspective because perspective itself was a type of algorithm with step-by-step procedures that were easily imitated by a computer [3]. At the same time, however, technology associated with the digital has invented several other possible ways to re-present reality, and because of this, perspective is now only one of many tools used in digital reproductions of reality.

As a result of this divergence from sight, a battle exists between those who believe that digital technology, including virtual reality (VR), subverts and diminishes the physical experience of body and space and those who believe that VR extends those physical experiences. As the dependence on the actual physical eye diminishes and the emphasis on Renaissance perspective becomes leveled, what happens to cultural, scientific and artistic notions of reality and reality's representations?

The following, by Kevin Robins, reflects the "postmodern" sentiment that physical experience is consumed by VR:

In the space of simulations and virtual reality, the "user" is immersed in a dematerialized and surrogate reality that has no apparent relation to the "real world." . . . His existence in this alternative space is disembodied, and any engagement with the real world (that is, tele-operation) is indirect, mediated through a screen or some other imaging technology [4].

Robins's camp argues that VR necessitates a disembodied participant, one whose experience, it is implied, is secondary because of the mediated structure of VR. Vivian Sobchack reiterates that virtual environments reflect a "desire to escape both the human body and the human world" [5].

While scientists have rejoined that sickness, death and hunger make it impossible to deny the importance of the physical body, digital artists Novak and Davies have countered this conception of disembodiment with a more theoretical exploration of the concepts of space and lived experience as mediated by VR [6]. For them, this virtual mediation is not in binary opposition to the physical world but rather a new way of thinking about physicality. The result is a hybrid of the physical and the virtual. This hybrid, though it does not subsume the physical, does revise it, changing our contemporary notions of reality and perception in radical ways. In relation to these artists, Leonardo's scientific resistance to Renaissance perspective can be seen as a preliminary heralding of such radical revisions of optics and representation.

Marcos Novak's response to those who see the digital world as a subversion of the physical world is skeptical: "Cyberspace, in its many forms, will not replace physical space. Rather, the two will merge into the amalgam already forming under names such as augmented reality and intelligent environments" [7]. Novak's works, or transarchitectures, are experiments with structures built in cyberspace (Color Plate B). Novak coined the term transarchitecture, which stems out of his earlier term liquid architecture, denoting "architecture whose form is contingent on the interests of the beholder" [8]. Because the programming for the forms in transarchitectures is not fixecl, each viewer will have a different experience in viewing. Thus, the viewer's perception is emphasized rather than undermined.

To create transarchitectures, Novak constructs mathematical models and generative procedures that are determined by unrelated variables. As Novak explains, "Each variable or process is a 'slot' into which an external influence can be mapped, either statically or dynamically" [9]. Novak's focus is not on the manipulation of objects so much as on "the manipulation of relations, fields, and higher dimensions" [10]. Novak's shift in attention marks a literalization of the non-Euclidean geometry Einstein insisted on as an augmentation of Newtonian physics, which he claimed failed to consider the real though imperceptible curvature of space. Novak's goal is to physically reproduce the non-Euclidean theory of the "curvature of space itself" [11]. For example, in one project Novak digitally curves the space in which he places a torus. As the space becomes progressively curved, the torus appears to become warped even though it is itself unchanged: Novak emphasizes: "The important point is this: in the subsequent images, it is not the torus that is deformed, but the space that the torus is embedded in—space itself is being curved and sculpted. The torus itself [in the initial stages] is undeformed" [12].

Transarchitectures belong to a larger body of architecture labeled parametric [13]. The implication of this type of architecture is that the design does not necessitate stable forms. Transarchitectures, then, are very much acts of indeterminacy. Branko Kolarevic points out that understanding and accepting indeterminate architecture has been difficult for architects trained in the certainties of Euclidean geometry and for the masses who find the idea incomprehensible [14]. Perez Gomez and Louise Pelletier respond to such resistance by insisting the accidental is a necessary solution to computer graphics systems' imposition of "homogenous space that, is inherently unable to combine different structures of reference" [15]. Novak's dynamic manipulation of design allows for the degree of indeterminacy that transforms space from a representational tool to a generative tool. Kolarevic calls this type of transformation digital morphogenesis [16] .

According to Novak, transarchitectures represent what a world of information might look like while at the same time showing how that world intersects with the physical world. This intersection, he claims, helps to overcome assumptions made about the physical world that are becoming increasingly suspect based on contemporary experience. For example, space is not necessarily a binary equivalent to either solid or void; likewise, people can now be in more than one place at one time. Because the concept of space is changing with the advent of the digital, Novak and other cyber-architects argue, "The development of temporally simultaneous activities in spatially discontinuons locations calls for a different imagination of presence and the shape of urban timespace" [17].

Novak's transarchitectures seek a newly shaped urban time-space by experimenting with the fourth dimension. As Alan Liu explains, Novak programs four-dimensional, algorithmic architectural shapes that mutate in time. From these 4D shapes, he extracts 3- or 2D "snapshots" by using 3D rapid prototyping or 2D imaging. This process results in a "reduced-dimension data pour from a higher-dimensional reality designed to elicit what Novak terms allogenetic, truly alien aesthetics," which move beyond neo-romantic notions of transcendence [18] (Fig. 1). As Novak creates these higher dimensions, objects in these spaces appear to become more and more warped or altered from their original forms. These objects, however, remain unchanged even though the alteration of their environment makes it appear that they have been warped. According to Bernard Cache, as a result of this play with dimension, space ceases to be a ground for the presentation of given elements, and geography ceases to be a context for building. The final result is that buildings are no longer seen as "discrete elements" but as topological operators or spatial manipulators that include space as part of the architectural building, crossed by different dimensions [19]. Because these "crossings" or connections are variable for every viewer, the space is differentially shaped.

Novak's conception of the 4th dimension includes the notion that space has also morphed in the digital world to account for time. As Novak explains, transarchitectures "lead to the re-problematization of time as an active element of architecture at the scale of the cognitive and musical, not just the historic, political or economic event" [20]. Because of its juxtaposition of space and time or space as time, transarchitectures are the realization of an alternative architectural poetics that looks past the "static depiction of objects and surfaces to the description of latent information fields" [21]. The result of such work is a marked shift from form and space to process and field.

In order to shift from past static description of objects and surfaces, Novak argues it is imperative to set aside Alberti's tools (linear perspective) as "beautiful, but finally nostalgic vestiges of another era" [22]. To move toward descriptions of latent information fields instead, we must consider what the physical world has already shown us. As Novak states in his epigraph above, the air surrounding us is permeated by intersecting waves of information: electromagnetism, light, pressure and body heat. "We already inhabit an invisible world of shapes, an architecture of latent information that is modulated by our every breath and transmission" [23].

DAVIES'S OSMOSE: DISSOLUTIONS OF BOUNDARIES

Digital still image captured during immersive perfromance of the virtual environment Ephémère.

Char Davies's Osmose (1995) is physically quite different from Novak's transarchitectures, but it similarly emphasizes the increasingly blurred lines between lived and virtual experiences. Also comparable to transarchitectures, Osmose emphasizes the intersecting permeations between viewer and viewed as underscored in VR. Like transarchitectures, Osmose emphasizes the specificity of the viewer's (Davies prefers immersant's) experience as a lived process rather than a static, disembodied one and departs from dependence on Renaissance perspective in order to challenge modem notions of space. The name Osmose was derived from osmos (Greek), meaning "to push"—a biological process involving passage from one side of a semipermeable cellular membrane to another. The term, as well as the VR environment, is about the dissolution of boundaries.

In order to emphasize the porous borders between lived experience and virtual experience, viewer and viewed, Davies grounds Osmose in the immersant's breath and balance and uses semi-transparent graphics to create perceptual ambiguity. Osmose is an immersive interactive environment in which the immersant wears a stereoscopic head-mounted display and a vest that trracks breathing and balance. The user interface is an immersion in a 360° space [24]. To move up, the immersant breathes in; to move clown he/she breathes out; to move in any given direction, the immersant leans in that direction. By making virtual experience contingent upon the immersant's body, Osmose registers a dissent from those who, like Simon Penny, argue that in VR experiences "one leaves the body at the door while the mind goes wandering, unhindered by the physical body" [25].

Char Davies, Osmose (1995), Forest Grid

Digital still image captured during immersive perfromance of the Osmose virtual environment.

Beyond underscoring the immersant's body as the contingency on which movement is based, Osmose resists the disembodiment of the participant by making the embodied participant part of a dual exhibit for other viewers (Fig. 2). The immersant is backlit in silhouette, with what he/she is viewing displayed on the opposing wall. Thus, the environment and the body of the immersant share a parallel billing, which emphasizes the shared significance of each as well as the process itself of being immersed in Osmose.

The structure of Osmose begins with the Cartesian 3D grid (Fig. 3), as if to emphasize the VR environment as itself rather than as a substitute for lived experience. Depending on the viewer's breath and movement, he/she may travel anywhere within the 12 world-spaces that compose the topology of Osmose (Fig. 4). These 12 world-spaces are mostly based upon "metaphorical aspects of nature." They include Clearing, Forest, Tree, Leaf, Cloud, Pond, Subterranean Earth and Abyss. There is also a "substratum," Code, which contains much of the software used to create the worlds, and a "substratum," Text, a space consisting of quotes from the artist and relevant texts on technology, the body and nature [26]. Although Osmose uses the natural world as a rnodel for its environment, it is not meant to directly imitate the actual physical space of those environments; rather, it seeks to imitate the sense of nature while preserving the unique qualities of VR in order to lead the viewer to a similar but original experience of reflection of self and environment. In this way, Osmose suggests that Cartesian notions of space and illustrative realism can be "replaced by more evocative alternatives" [27].

Davies's work, like Novak's, also resists modern notions of space that serve as metaphors for concepts and experiences of separation. Such metaphors, Roger Jones argues, are a direct result of the laws of perspective and geometry, which are a "codified summary of our normal experience of alienation, unique iclentity and unrelatedness" [28]. Perspective has been abstracted into empty voids we call space. For Davies, VR environments allow her to challenge that notion specifically by challenging perspective and what she calls the "hard-edged-objects-in-empty-space syndrome" that has issued as a byproduct of a "never-ending quest for visual realism" [29].

Char Davies, Osmose, virtual environment world schematic (1995).

Davies's project, she explains, evolved from many years of artistic research based on her own perception of light and space. Based on her observations, she uses semi-transparent graphics (Color Plate C), which emphasize Merleau-Ponty's notion that "the world is all around me, not in front of me" [30]. The decision is also grounded in the resistance of "hard-edged-objects-in-empty-space." Semi-transparency resists the theory associated with VR environments that suggest the participant is visiting a foreign environment that is not physically connected to him/her. As with the use of breath, semi-transparency emphasizes the inability to distinguish between participant and environment in such binary terms. As Davies explains, "With the flux and flow, boundaries between self and world dissolve and intermingle" [31]. Toward the same end, using breath as the motor for Osmose, Davies depends on breath "as a potent tool for overcoming dualism": "Physiologically, respiration stands at the threshold of the ecstatic and visceral...inside and outside...are relativized, porous, each time one takes a breath" [32].

Novak's and Davies's approaches to optics at the intersection of physical experience and VR are parallel to Leonarclo's in their insistence that computer graphics' use of linear perspective has reiterated a mathematics that does not account for the profound relationship of objects, whether lived or represented, to one another. Leonardo's emphasis on the blurred boundaries between objects offers a prototype that technology has only now begun to match. For Davies, the digital has allowed a literalization of porous boundaries between viewer and environment. As Annick Bureaud has expressed it: "With Osmose we are within the work but, more powerfully, the work is within ourselves that we exhale with our breath, intimacy, interpenetration of the work and the I" [33]. For Novak, the digital allows for indeterminate architecture, and the ability to communicate that architecture, according to Novak, is the ability to transmit space—"the most radical gesture" [34].

At this juncture, the possibilities for optics are by no means exhausted, but they will continue to be revised with the same skepticism and ingenuity with which Leonardo approached linear perspective. As technology catches up with optical theory, the results will be revolutionary. Novak argues, "We will discover the alien that is so near as to be outlandish. We will become citizens in the spaces of our varied consciousnesses" [35]. Even more extremely, N. Katherine Hayles imagines that the perpetuation of virtual realities will lead to a future in which it is impossible to "distinguish meaningfully between the biological organism and the information circuits in which it is enmeshed" [36]. These notions do not indicate that the body will be sacrificed to digital technology, nor are they science fiction. They are the culmination of radical revisions of Renaissance perspective and the resulting theories of space and physical experience that endured until the advent of digital technology.

Acknowledgment

Special thanks to Char Davies and Marcos Novak for invaluable elucidation and permission to reproduce photographs of their work.

References and Notes

1. Interestingly, in Perspective as Symbolic Form, Panofsky argues contrary to Leonardo that linear perspective's effect and intended purpose is to "realize in the representation of space precisely that homogeneity and boundlessness foreign to the direct experience of space." Leonardo believed that linear perspective's great downfall was the inability to so.

6. Although outside the scope of this paper, digital technology other than VR similarly reflects Leonardo's preemptive theory on objects' profound connections. Consider, for example, how bar codes and RFID (radio frequency ID) reflect Leonardo's description of object connections: "The air is full of infinite straight and radiating lines intersected and interwoven with one another." L. Da Vinci. Notebooks, trans. Jean Paul Richter (1880). Other digital technology is equally reflective. New technology allows cell phones and GPS systems to track cargo containers anywhere in the world. Even more advanced, continued study of electron spin resonance is determining whether the atomic spin patterns of molecules could be sensed and used for identification proposes.

24. While, in 1998, Hubert Damisch argued that we can never escape the system of perspective with the example that computers and cameras still depend on a viewer/stage relationship, VR's use of a 360<deg> space may problematize or at least change the language of Damisch's theory. Paraphrase gathered from October Round Table, 1998.

Glossary

digital morphogenesis — translated from Greek, morphogenesis is shape creation. It is primarily associated with biological development, but in this case is borrowed to describe computationally based processes of form origination and transformations [37]. Of the various types of digital morphogenesis, Novak's work fits into the parametric category.

immersant — Davies's preferred term for the participant in her VR environments. Immersant more accurately describes the participant and his/her complete submersion in a different world, as if going under water.

torus (plural: torii) — a surface created by revolving a circle in 3D space about an axis coplanar with the circle. Examples include: doughnuts and inner tubes.

transarchitectures — architectures that are generative and variable and transcend/connect the boundaries of physical and virtual materials. As described by Marcos Novak: "In short, we conceive algorithmically (morphogenesis); we model numerically (rapid prototyping); we build robotically (new tectonics); we inhabit interactively (intelligent space); we telecommunicate instantly (pantopicon); we are informed immersively (liquid architectures); we socialize nonlocally (nonlocal public domain); we evert virtuality (transarchitectures)."

Manuscript received 14 August 2007.

Cami Nelson is a doctoral student in poetry and an instructor in the engineering department at the University of Utah.

This article may include minor changes from the original publication in order to improve legibility and layout consistency within the Immersence Website. † Significant changes from the original text have been indicated in red square brackets.